2019-05-25T13:00:39ZBounded solutions of self-adjoint second order linear difference equations with periodic coefficientshttp://hdl.handle.net/2117/114994
Bounded solutions of self-adjoint second order linear difference equations with periodic coefficients
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
In this work we obtain easy characterizations for the boundedness of the solutions
of the discrete, self–adjoint, second order and linear unidimensional
equations with periodic coefficients, including the analysis of the so-called discrete
Mathieu equations as particular cases.
2018-03-09T11:45:32ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María JoséIn this work we obtain easy characterizations for the boundedness of the solutions
of the discrete, self–adjoint, second order and linear unidimensional
equations with periodic coefficients, including the analysis of the so-called discrete
Mathieu equations as particular cases.Second order linear difference equationshttp://hdl.handle.net/2117/112719
Second order linear difference equations
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
We provide the explicit solution of a general second order linear difference equation via the computation of its associated Green function. This Green function is completely characterized and we obtain a closed expression for it using functions of two–variables, that we have called Chebyshev functions due to its intimate relation with the usual one–variable Chebyshev polynomials. In fact, we show that Chebyshev functions become Chebyshev polynomials if constant coefficients are considered.
2018-01-12T11:42:21ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María JoséWe provide the explicit solution of a general second order linear difference equation via the computation of its associated Green function. This Green function is completely characterized and we obtain a closed expression for it using functions of two–variables, that we have called Chebyshev functions due to its intimate relation with the usual one–variable Chebyshev polynomials. In fact, we show that Chebyshev functions become Chebyshev polynomials if constant coefficients are considered.Vertex-disjoint cycles in bipartite tournamentshttp://hdl.handle.net/2117/111583
Vertex-disjoint cycles in bipartite tournaments
González Moreno, Diego; Balbuena Martínez, Maria Camino Teófila; Olsen, Mika
Let k=2 be an integer. Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k-1 contains k vertex-disjoint cycles. Recently Bai, Li and Li proved this conjecture for bipartite digraphs. In this paper we prove that every bipartite tournament with minimum out-degree at least 2k-2, minimum in-degree at least 1 and partite sets of cardinality at least 2k contains k vertex-disjoint 4-cycles whenever k=3. Finally, we show that every bipartite tournament with minimum degree d=min(d+,d-) at least 1.5k-1 contains at least k vertex-disjoint 4-cycles.
2017-12-05T14:22:23ZGonzález Moreno, DiegoBalbuena Martínez, Maria Camino TeófilaOlsen, MikaLet k=2 be an integer. Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k-1 contains k vertex-disjoint cycles. Recently Bai, Li and Li proved this conjecture for bipartite digraphs. In this paper we prove that every bipartite tournament with minimum out-degree at least 2k-2, minimum in-degree at least 1 and partite sets of cardinality at least 2k contains k vertex-disjoint 4-cycles whenever k=3. Finally, we show that every bipartite tournament with minimum degree d=min(d+,d-) at least 1.5k-1 contains at least k vertex-disjoint 4-cycles.Triangular matrices and combinatorial recurrenceshttp://hdl.handle.net/2117/109153
Triangular matrices and combinatorial recurrences
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
2017-10-25T12:18:33ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María JoséCharacterizing identifying codes through the spectrum of a graph or digraphhttp://hdl.handle.net/2117/108920
Characterizing identifying codes through the spectrum of a graph or digraph
Balbuena Martínez, Maria Camino Teófila; Dalfó Simó, Cristina; Martínez Barona, Berenice
2017-10-20T12:13:09ZBalbuena Martínez, Maria Camino TeófilaDalfó Simó, CristinaMartínez Barona, BereniceFunciones de green en redes productohttp://hdl.handle.net/2117/107904
Funciones de green en redes producto
Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida
En esta comunicación presentaremos la versión discreta del método de separación
de variables para determinar la función de Green de redes producto en términos
de la función de Green de uno de las redes factores y los autovalores y autofunciones de un operador de Schrödinger de la otra red factor.
2017-09-22T10:02:52ZArauz Lombardía, CristinaCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosMitjana Riera, MargaridaEn esta comunicación presentaremos la versión discreta del método de separación
de variables para determinar la función de Green de redes producto en términos
de la función de Green de uno de las redes factores y los autovalores y autofunciones de un operador de Schrödinger de la otra red factor.Cálculo de la inversa de una matriz de Jacobihttp://hdl.handle.net/2117/107901
Cálculo de la inversa de una matriz de Jacobi
Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
En este trabajo aportamos las condiciones necesarias y suficientes para
la invertibilidad de las matrices de Jacobi y calculamos explícitamente su inversa. Las técnicas que utilizamos están relacionadas con la soluciones de problemas de contorno que pueden calcularse gracias a avances recientes en el estudio de ecuaciones en diferencias lineales de segundo orden.
2017-09-22T09:43:02ZEncinas Bachiller, Andrés MarcosJiménez Jiménez, María JoséEn este trabajo aportamos las condiciones necesarias y suficientes para
la invertibilidad de las matrices de Jacobi y calculamos explícitamente su inversa. Las técnicas que utilizamos están relacionadas con la soluciones de problemas de contorno que pueden calcularse gracias a avances recientes en el estudio de ecuaciones en diferencias lineales de segundo orden.Resistive distances on networkshttp://hdl.handle.net/2117/107459
Resistive distances on networks
Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Mitjana Riera, Margarida
2017-09-06T12:18:58ZCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosMitjana Riera, MargaridaDiscrete inverse problem on gridshttp://hdl.handle.net/2117/107406
Discrete inverse problem on grids
Arauz Lombardía, Cristina; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos
In this work, we present an algorithm to the recovery of the conductance of a n –dimensional grid. The algorithm is based in the solution of some overdetermined partial boundary value problems defined on the grid; that is, boundary value problem where the boundary conditions are set only in a part of the boundary (partial), and moreover in a fix subset of the boundary we prescribe both the value of the function and of its normal derivative (overdetermined). Our goal is to recover the conductance of a n –dimensional grid network with boundary using only boundary measurements and global equilibrium conditions. This problem is known as inverse boundary value problem . In general, inverse problems are exponentially ill–posed, since they are highly sensitive to changes in the boundary data. However, in this work we deal with a situation where the recovery of the conductance is feasible: grid networks. The recovery of the conductances of a grid network is performed here using its Schr ¨odinger matrix and boundary value problems associated to it. Moreover, we use the Dirichlet–to–Robin matrix, also known as response matrix of the network, which contains the boundary information. It is a certain Schur complement of the Schr ¨odinger matrix. The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications.
2017-09-05T13:00:41ZArauz Lombardía, CristinaCarmona Mejías, ÁngelesEncinas Bachiller, Andrés MarcosIn this work, we present an algorithm to the recovery of the conductance of a n –dimensional grid. The algorithm is based in the solution of some overdetermined partial boundary value problems defined on the grid; that is, boundary value problem where the boundary conditions are set only in a part of the boundary (partial), and moreover in a fix subset of the boundary we prescribe both the value of the function and of its normal derivative (overdetermined). Our goal is to recover the conductance of a n –dimensional grid network with boundary using only boundary measurements and global equilibrium conditions. This problem is known as inverse boundary value problem . In general, inverse problems are exponentially ill–posed, since they are highly sensitive to changes in the boundary data. However, in this work we deal with a situation where the recovery of the conductance is feasible: grid networks. The recovery of the conductances of a grid network is performed here using its Schr ¨odinger matrix and boundary value problems associated to it. Moreover, we use the Dirichlet–to–Robin matrix, also known as response matrix of the network, which contains the boundary information. It is a certain Schur complement of the Schr ¨odinger matrix. The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications.Green’s kernel for subdivision networkshttp://hdl.handle.net/2117/107370
Green’s kernel for subdivision networks
Carmona Mejías, Ángeles; Mitjana Riera, Margarida; Monsó Burgués, Enrique P.J.
2017-09-04T13:20:25ZCarmona Mejías, ÁngelesMitjana Riera, MargaridaMonsó Burgués, Enrique P.J.